Countdown plus problems II

Discus: SAT/ACT Tests and Test Preparation: June 2004 Archive: Countdown plus problems II
 By Strider (Strider) on Wednesday, June 16, 2004 - 02:24 pm: Edit

there! post away~

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 02:30 pm: Edit

Here is another problem that I am going to post. It is a probability question.

Assorted fruit packs come in 3 types: Type A containing 2 apples, 2 pears and 1 orange, Type B containing 3 apples, 1 pear and 2 oranges, and Type C containing 1 apple and 3 pears. Tom randomly picks one of the types of packets and randomly selects a piece of fruit from the packet. Find the probability if he gets a pear, that it came from a Type B packet. Give the answer in exact rational form.

 By Strider (Strider) on Wednesday, June 16, 2004 - 02:32 pm: Edit

ughh...i'm terrible at probabilities...i'm guessing, though it's probably not right, is the answer..1/18?

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:32 pm: Edit

ets, how does one derive -b/2a again? i don't think i have seen it before.

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 02:33 pm: Edit

The answer is not 1/18 -- keep on trying.

 By Shizpit (Shizpit) on Wednesday, June 16, 2004 - 02:34 pm: Edit

1/6 i think

 By Simei (Simei) on Wednesday, June 16, 2004 - 02:35 pm: Edit

1/15?

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:35 pm: Edit

1/18

1/3 for random packet
1/6 to get a pear

 By Hollaratme (Hollaratme) on Wednesday, June 16, 2004 - 02:36 pm: Edit

ets rep i wnt my score andi cant wait!

 By Strider (Strider) on Wednesday, June 16, 2004 - 02:36 pm: Edit

yeah...i got 1/15 on this try,too...thou still not sure

 By Shizpit (Shizpit) on Wednesday, June 16, 2004 - 02:37 pm: Edit

no it says he got a pear already then it says whats the probability it came from packat b well b has 1 pear and the other 2 combined have 5 so 1/6

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:37 pm: Edit

1/45

 By Strider (Strider) on Wednesday, June 16, 2004 - 02:37 pm: Edit

nevermind

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 02:38 pm: Edit

Keep trying -- this one is tricky -- it requires the use of the principle of conditional probability. Draw a tree diagram on a separate sheet of paper to help you visualize the possibilities. Those are my only hints.

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:38 pm: Edit

1/15 x 1/3 = 1/45

right?

 By Adidasty (Adidasty) on Wednesday, June 16, 2004 - 02:38 pm: Edit

1/18 is the answer, look at AltF4's reasoning.

 By Sirhcv (Sirhcv) on Wednesday, June 16, 2004 - 02:38 pm: Edit

1/6?

 By Shizpit (Shizpit) on Wednesday, June 16, 2004 - 02:39 pm: Edit

unless of course the answer is 1/3 bc it there are only 3 packets...lol don't think thats right though...i am stickign with 1/6

 By Shizpit (Shizpit) on Wednesday, June 16, 2004 - 02:40 pm: Edit

oh he picked the pack before he picked the pear so it 1/3

 By Strider (Strider) on Wednesday, June 16, 2004 - 02:40 pm: Edit

2/75?

 By Adidasty (Adidasty) on Wednesday, June 16, 2004 - 02:41 pm: Edit

wait wait........there are altogether 6 pears. 5 are from A and C, that means the probability of his getting the one from B is 1/6.

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 02:41 pm: Edit

AltF4: You only found the P(B and pear). You still need to find the probability of something else in order to correctly answer the question.

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:41 pm: Edit

no
but u have to get a pear first from the entire population, then you have to multiply that by the packet, which narrows down the probability, the conditions have to occur in order, so my first one was wrong

 By Strider (Strider) on Wednesday, June 16, 2004 - 02:42 pm: Edit

wait...i think it's 1/15...ther's 15 fruits in total and only one pear would satisfy the condition of coming from packet B

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:43 pm: Edit

i think we're all wrong

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:44 pm: Edit

the problem in itself is confusing, because does he do the packet first or the pear first?

 By Shizpit (Shizpit) on Wednesday, June 16, 2004 - 02:45 pm: Edit

i am taking it step by step first says he picks a basket so its 1/3 then a pear from teh total thats 6/15 then its from basket b thats 1/6 so i get 1/3 * 6/15 * 1/6 = 1/45 but he said thats wrong so i dunno haven't taken stats yet tahts next year woohoo ap stats sounds like fun

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:46 pm: Edit

1/45 x 1/6 for being a pear in that same packet

 By Shizpit (Shizpit) on Wednesday, June 16, 2004 - 02:46 pm: Edit

when i first read it it sounded like he picked the packet then the pear and now it wants to nkow the probability that thhe pear is from packet b and if it was like that then it would be 1/6 but that obviously isn't wat its askign

 By Strider (Strider) on Wednesday, June 16, 2004 - 02:46 pm: Edit

4/25?

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:47 pm: Edit

the conditions are

it has to be a pear 1/15
it has to come from the packet 1/3
it has to be a pear in that same packet 1/6

1/270???

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:48 pm: Edit

nah, that's unrealistic, disregard my last post.

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 02:49 pm: Edit

Here is the formula that you need to solve this problem. P(B|pear) = the probability that Tom picked from the Type B packet GIVEN THAT it is a pear.

P(B|pear) = P(B and pear)/P(pear)

This question should be a lot easier to solve now.

 By Shizpit (Shizpit) on Wednesday, June 16, 2004 - 02:50 pm: Edit

u messed up bc it has to be a pear is 6/15 not 1/15 bc there is 6 pears altf4 just to let u know

 By Strider (Strider) on Wednesday, June 16, 2004 - 02:51 pm: Edit

well...isn't that 1/15 then?

 By Shizpit (Shizpit) on Wednesday, June 16, 2004 - 02:51 pm: Edit

if put it that way i get 5/12 but i dunno this problem is all messed up

 By Adidasty (Adidasty) on Wednesday, June 16, 2004 - 02:53 pm: Edit

5/6. period. there

 By Shizpit (Shizpit) on Wednesday, June 16, 2004 - 02:53 pm: Edit

just give us the answer ets

 By Silverfish (Silverfish) on Wednesday, June 16, 2004 - 02:53 pm: Edit

oh and ETSrep...do ya kno how sensitive those machines are? cuz i just had time to mark half the bubble for one of the questions on iic

 By Adidasty (Adidasty) on Wednesday, June 16, 2004 - 02:54 pm: Edit

how bout 1/3. i say 1/3 now

 By Adidasty (Adidasty) on Wednesday, June 16, 2004 - 02:54 pm: Edit

how bout 1/3. i say 1/3 now

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:55 pm: Edit

ets, am i screwed if i haven't gotten any of urs correct?

 By Wrathofgod64 (Wrathofgod64) on Wednesday, June 16, 2004 - 02:55 pm: Edit

i sincerely hope the new sat doesn't have problems like these

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:58 pm: Edit

P(B and pear) = 1/45

divided by

P(pear) = 6/15
right?

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 02:59 pm: Edit

1/45
----
6/15

= 1/18?

 By Strider (Strider) on Wednesday, June 16, 2004 - 02:59 pm: Edit

wait... should be 5/12 i think

 By Wrathofgod64 (Wrathofgod64) on Wednesday, June 16, 2004 - 03:02 pm: Edit

i got 1/6

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 03:03 pm: Edit

5/12 is only the probability of a pear in the entire collectiveg group, it doesn't even take into account the probability of packet B element.

 By Sirhcv (Sirhcv) on Wednesday, June 16, 2004 - 03:03 pm: Edit

5/21...but I ran a simulation on my calculator =P
Even then I'm not sure if its right

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 03:05 pm: Edit

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 03:06 pm: Edit

ETS WHERE ARE YOU?

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 03:07 pm: Edit

 By Silverfish (Silverfish) on Wednesday, June 16, 2004 - 03:11 pm: Edit

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 03:15 pm: Edit

Finding the probability of P(B and pear) was the first step, which is 1/3 * 1/6 = 1/18.

The next step was finding P(pear) = P(A and pear) + P(B and pear) + P(C and pear) = (1/3 * 2/5) + (1/3 * 1/6) + (1/3 * 3/4) = 79/180.

Plug those values into the formula given for conditional probability = P(B|P) = P(B and pear)/P(pear) = (1/18)/(79/180) = 10/79.

 By Adidasty (Adidasty) on Wednesday, June 16, 2004 - 03:32 pm: Edit

give me a break. if they put those on the new SAT we'll get nice 600's . those kinda of problems dont test your intrinsic math ability (as the old SAT I does), these kind of problems see how many formulas youve memorized and stored on your calculator. Yeah, ill remember the formula for conditional probability along with every other formula there is out there for the New SAT's huh? while im at it ill go memorize the proof for De Moivre's Theorem of complex numbers. dang man, give me some math reasoning questions, not these things. you wont need to remember how to translate f(x) to a new area on the graph daily (like asked to do on this new SAT), but SAT I math has real everyday applications. thats how i like it.

 By Adidasty (Adidasty) on Wednesday, June 16, 2004 - 03:33 pm: Edit

if theyre gonna do this BS, they should do it on a new test, Math IIIC. make it advanced/difficult precalculus with calculus 1 topics like implicit differentiation and some antiderivatives. say I if you agree with making a Math IIIC test. lol

 By Sirhcv (Sirhcv) on Wednesday, June 16, 2004 - 03:43 pm: Edit

uuuuuh saying the formula for conditional probability is memorized seems a little to simple. I'm sure someone intelligent with a moderate background in probability would be able to solve it. It seems to me though that probability isnt taught to a very high degree is most schools.. And remeber the SAT is curved..

And even if you wanted an IIIC it would never be developed in time for you to take it..

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 03:50 pm: Edit

i agree that ETS, the company, should die. they're tests don't measure jack. grades are a better measurement of student performance over the years than a stupid 3 hour test(of course, the grades are compared to those in the same class from the same school; if there's grade inflation, that's another story) . it only favors those with a narrow band of intelligence out of the many forms of intelligence that can all be used to suceed in college.

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 03:50 pm: Edit

I agree with creating a Math IIIC, but then that would be redundant in conjunction with the AP calculus test.

 By Wrathofgod64 (Wrathofgod64) on Wednesday, June 16, 2004 - 03:57 pm: Edit

well there are a lot of sat 2's that have corresponding ap's if that's wat u mean.

 By Strider (Strider) on Wednesday, June 16, 2004 - 03:58 pm: Edit

wow...after coming back from babysitting my sister, the direction of the thread has turned compeletely! calm down guys, remember we are just here doing interesting math problems while passing time~
and how about another problem ETSrep?

 By Strider (Strider) on Wednesday, June 16, 2004 - 04:13 pm: Edit

where are you ETSrep? we need more problems~~

 By Strider (Strider) on Wednesday, June 16, 2004 - 04:24 pm: Edit

sign~ i see some of u lucky ppl already have ur scores~~ mine are not up yet...just hope they'll be up t/m...last time i had to wait one extra week for them

 By Adidasty (Adidasty) on Wednesday, June 16, 2004 - 04:25 pm: Edit

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 04:29 pm: Edit

A fence for a rectangular garden with one side against an existing wall is constructed by using 50 feet of fencing. What is the maximum area that can be enclosed?

 By Strider (Strider) on Wednesday, June 16, 2004 - 04:34 pm: Edit

er...312.5?

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 04:39 pm: Edit

Here is an easy question: When students are anxious to receive their SAT scores, 1 day seems like a thousand years. If 1 day = 1000 years, then how many seconds old is a 12-year-old child? (Round your answer to the nearest whole number.)

 By Strider (Strider) on Wednesday, June 16, 2004 - 04:46 pm: Edit

1037?

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 04:50 pm: Edit

You are 2 for 2 Strider.

 By Strider (Strider) on Wednesday, June 16, 2004 - 04:53 pm: Edit

more please~~ and where did the others go? i'm really bored right now (doin nothing but refreshing the status page)

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 04:57 pm: Edit

x^3 < x^2 - x + 1

 By Hollaratme (Hollaratme) on Wednesday, June 16, 2004 - 04:59 pm: Edit

false

lol

 By Strider (Strider) on Wednesday, June 16, 2004 - 05:01 pm: Edit

X<1?

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 05:02 pm: Edit

There is one curveball: (x-1)(x^2 + 1) < 0. How do you approach (x^2 + 1) < 0?

This question will test your mathematical abilities/reasoning and not so much SAT math skills.

 By Strider (Strider) on Wednesday, June 16, 2004 - 05:05 pm: Edit

i thought x^2 +1 is bound to be greater than zero so i just disregarded it...is there more to it?

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 05:09 pm: Edit

There is an imaginary part -- but it gets ugly.

 By Strider (Strider) on Wednesday, June 16, 2004 - 05:18 pm: Edit

-i<x<i?

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 05:22 pm: Edit

How do you find the spare time to be sitting at your computer all day waiting for me to give you additional math questions?

Better question yet, why have I been giving you math problems since yesterday?

This is best explained by Einstein's paradox: As the relativistic kinetic energy of a particle approaches the speed of light, its mass decreases without bound in the negative y direction.

The author's statement of Einstein's paradox is:
(A) regretful
(B) accurate
(C) intuitive
(D) sarcastic
(E) defiant

 By Strider (Strider) on Wednesday, June 16, 2004 - 05:29 pm: Edit

lol...(A)?

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 05:35 pm: Edit

Actually, it is (D) sarcastic. My tone is sarcastic because, first of all, the explanation of Einstein's paradox is totally opposite of what he believed. Second, it has nothing to do with the questions I posed in the beginning.

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 05:39 pm: Edit

Am I:

(A) an ETS representative
(B) an insane math professor
(C) a high-school student
(D) a college student
(E) a robot designed by NASA

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 05:42 pm: Edit

none of the above. ur a fag

 By Kewlkiwi102 (Kewlkiwi102) on Wednesday, June 16, 2004 - 05:43 pm: Edit

you are D, a college student doing a project on behavioral patters on mildly-OCD, or just plain obsessive teenagers. CC is the perfect place to find em.

 By Kewlkiwi102 (Kewlkiwi102) on Wednesday, June 16, 2004 - 05:45 pm: Edit

.

 By Laurenh87 (Laurenh87) on Wednesday, June 16, 2004 - 05:47 pm: Edit

LOL Kewlkiwi!

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 05:49 pm: Edit

no, he's a fag

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 05:49 pm: Edit

Kewlkiwi102 -- you guessed correctly. I am a college student here at Rutgers studying what obsession can cause a person to do. For example, many people disputed the fact that I was an ETS rep. However, many respected me, even if I truly wasn't an ETS rep. They saw me as some "individual" who was helping them pass their time while they were anxiously awaiting their scores.

TheGumby made an interesting point: The thing is... Part of me knows ETSRep is fake.. But still, this is such a frantic/stressful time that being able to ask someone questions (even though their answers are likely fabricated) is somewhat comforting...

This is the thesis of my project. Thank you for willingly participating in this research project. Your reactions were quite amusing.

 By Zbjz15 (Zbjz15) on Wednesday, June 16, 2004 - 05:50 pm: Edit

Now I can say I told you so.

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 05:52 pm: Edit

ok fine he's not a fag, i would have done the same thing.

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 05:52 pm: Edit

Why don't you get your Mods to run an IP check on me now, huh? Are you scared? Afraid that I might actually be an ETS representative who is playing with your mind? Afraid that I am now an ETS representative posing as a college student?

 By Strider (Strider) on Wednesday, June 16, 2004 - 05:52 pm: Edit

ha, cool~ so is ur study finished? can u still keep posting problems?

 By Jer728 (Jer728) on Wednesday, June 16, 2004 - 05:54 pm: Edit

We are not test mice! I hope ETS takes you down.

 By Theleet (Theleet) on Wednesday, June 16, 2004 - 05:54 pm: Edit

Ive seen this so many times on the internet. First somebody pretends to be somebody famous, or knows somebody famous. Then when their bluff is called, they save face by saying it was a "research" study, and they were playing everybody for that reason. In reality, none of its true.

 By Newt (Newt) on Wednesday, June 16, 2004 - 05:55 pm: Edit

PLEASE DONT LEAVE ME ETSDUDE1337-7.0. I LOVE U, SIGNED ME.

 By Newt (Newt) on Wednesday, June 16, 2004 - 05:55 pm: Edit

db post b/c i win

 By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 05:56 pm: Edit

If I keep posting problems, I will never get to catch up with my partying Peace out, and I might appear on this thread later.

 By Zbjz15 (Zbjz15) on Wednesday, June 16, 2004 - 05:59 pm: Edit

Don't be so proud of yourself, rutgers, haha.

 By Altf4 (Altf4) on Wednesday, June 16, 2004 - 06:00 pm: Edit

i doubt u will be partying

 By Newt (Newt) on Wednesday, June 16, 2004 - 06:01 pm: Edit

I have a question: if you could guess one number, what is this secret number. (there is a correct answer (2 actually)).

 By Newt (Newt) on Wednesday, June 16, 2004 - 06:04 pm: Edit

.

 By Hollaratme (Hollaratme) on Wednesday, June 16, 2004 - 06:05 pm: Edit

By Hollaratme (Hollaratme) on Wednesday, June 16, 2004 - 12:20 pm: Edit

ets rep will the scores come up today?

By Etsrep78328 (Etsrep78328) on Wednesday, June 16, 2004 - 12:23 pm: Edit

The chance that the scores come up today is like saying that the exact value of the square root of pi has been discovered.

some people scores came up today lol

 By Jer728 (Jer728) on Wednesday, June 16, 2004 - 06:08 pm: Edit

Wait, so he actually gave people false advice? That really isn't good, even if its for science.

 By Astrix (Astrix) on Thursday, June 17, 2004 - 01:39 am: Edit

He was pretty wise with his advice. So it's okay I guess.

I can't post any more curves coz my boss caught me doing it?!

Etsrep I'll miss you :-p Come again.

 By Joshjmgs (Joshjmgs) on Thursday, June 17, 2004 - 06:54 am: Edit

ETS finally updated my SAT IIs! w00h00!
Still no scores, but at least I know that they know I took the physics ^^

 By Etsrep78328 (Etsrep78328) on Thursday, June 17, 2004 - 07:20 am: Edit

I came again to visit -- but now I am known as the "lowly janitor." I shouldn't even bother posting anymore. Before, you thought I was amazing with those math problems, and now, you think I'm a complete idiot.

 By Sns22022 (Sns22022) on Thursday, June 17, 2004 - 08:57 am: Edit

Well guys. It's down to 7 hours until the official 4 PM. Hopefully sooner!

 By Etsrep78328 (Etsrep78328) on Thursday, June 17, 2004 - 09:08 am: Edit

By the way Sns22022 -- is it currently cloudy where you live?

 By Sns22022 (Sns22022) on Thursday, June 17, 2004 - 09:13 am: Edit

 By Varr (Varr) on Thursday, June 17, 2004 - 09:15 am: Edit

thats an easy call just look at the time

 By Etsrep78328 (Etsrep78328) on Thursday, June 17, 2004 - 09:15 am: Edit

I'm just wondering ...
I'm from the FBI put your hands up! You have the right to remain silent here and in federal court.

 By Varr (Varr) on Thursday, June 17, 2004 - 09:15 am: Edit

thats an easy call just look at the time